ParkerDMCH9HW
Nickolas Parker
10/08/2020
Introduction
This analysis looks at the topic of KNN, which stands for k-nearest neighbor. This type of algorithm is used to classify an object’s outcome based on their location in relationship to their space within a training set. This data set comes from the FuelEconomy.csv and looks at city miles per gallon, cylinders, engine displacement in liters(displ), and model year. In particular, the analyses looks how correctly fuel type for a vehicle is classified with a k of 1 and 5.
head(FuelEconomy)## # A tibble: 6 x 11
## city cylinders displ drive fuelType highway make model trans VClass year
## <dbl> <dbl> <dbl> <chr> <chr> <dbl> <chr> <chr> <chr> <chr> <dbl>
## 1 19 4 2 Rear-W~ Regular 25 Alfa ~ Spid~ Manu~ Two S~ 1985
## 2 9 12 4.9 Rear-W~ Regular 14 Ferra~ Test~ Manu~ Two S~ 1985
## 3 23 4 2.2 Front-~ Regular 33 Dodge Char~ Manu~ Subco~ 1985
## 4 10 8 5.2 Rear-W~ Regular 12 Dodge B150~ Auto~ Vans 1985
## 5 17 4 2.2 4-Whee~ Premium 23 Subaru Lega~ Manu~ Compa~ 1993
## 6 21 4 1.8 Front-~ Regular 24 Subaru Loya~ Auto~ Compa~ 1993dim(FuelEconomy)## [1] 38692 11table(FuelEconomy$fuelType)##
## CNG Diesel
## 60 977
## Gasoline or E85 Gasoline or natural gas
## 1287 20
## Gasoline or propane Midgrade
## 8 100
## Premium Premium and Electricity
## 11055 47
## Premium Gas or Electricity Premium or E85
## 28 125
## Regular Regular Gas and Electricity
## 24953 29
## Regular Gas or Electricity
## 3summary(FuelEconomy)## city cylinders displ drive
## Min. : 6.00 Min. : 2.000 Min. :0.60 Length:38692
## 1st Qu.:15.00 1st Qu.: 4.000 1st Qu.:2.20 Class :character
## Median :17.00 Median : 6.000 Median :3.00 Mode :character
## Mean :17.81 Mean : 5.745 Mean :3.32
## 3rd Qu.:20.00 3rd Qu.: 6.000 3rd Qu.:4.30
## Max. :58.00 Max. :16.000 Max. :8.40
## fuelType highway make model
## Length:38692 Min. : 9.00 Length:38692 Length:38692
## Class :character 1st Qu.:20.00 Class :character Class :character
## Mode :character Median :24.00 Mode :character Mode :character
## Mean :24.02
## 3rd Qu.:27.00
## Max. :61.00
## trans VClass year
## Length:38692 Length:38692 Min. :1984
## Class :character Class :character 1st Qu.:1992
## Mode :character Mode :character Median :2002
## Mean :2002
## 3rd Qu.:2011
## Max. :2019boxplot(city~fuelType, data = FuelEconomy)
boxplot(cylinders~fuelType, data = FuelEconomy)
boxplot(displ~fuelType, data = FuelEconomy)
boxplot(year~fuelType, data = FuelEconomy)
n=length(FuelEconomy$fuelType)
nt=36192
set.seed(1)
train <- sample(1:n,nt)x<-scale(FuelEconomy[,c(1,2,3,11)])
x[1:3,]## city cylinders displ year
## [1,] 0.2432124 -0.9928793 -0.9711933 -1.553615
## [2,] -1.8084528 3.5597809 1.1627078 -1.553615
## [3,] 1.0638784 -0.9928793 -0.8240277 -1.553615mean(x)## [1] -1.846242e-15sd(x)## [1] 0.9999903library(class)
nearest1 <- knn(train=x[train,],test=x[-train,],cl=FuelEconomy$fuelType[train],k=1)
nearest5 <- knn(train=x[train,],test=x[-train,],cl=FuelEconomy$fuelType[train],k=5)
plot(x[train,],col=FuelEconomy$fuelType[train],cex=.8,main="1-nearest neighbor")
points(x[-train,],bg=nearest1,pch=21,col=grey(.9),cex=1.25)
plot(x[train,],col=FuelEconomy$fuelType[train],cex=.8,main="5-nearest neighbors")
points(x[-train,],bg=nearest5,pch=21,col=grey(.9),cex=1.25)
pcorrn1=100*sum(FuelEconomy$fuelType[-train]==nearest1)/(n-nt)
pcorrn5=100*sum(FuelEconomy$fuelType[-train]==nearest5)/(n-nt)
pcorrn1## [1] 84.4pcorrn5## [1] 82.52numCorrn1=(pcorrn1/100)*n
PressQ1=((n-(numCorrn1*13))^2)/(n*12)
PressQ1## [1] 320630.2qchisq(.95,5) ## [1] 11.0705numCorrn5=(pcorrn5/100)*n
PressQ5=((n-(numCorrn5*13))^2)/(n*12)
PressQ5## [1] 305106.4pcorr=dim(10)
for (k in 1:10) {
pred=knn.cv(x,FuelEconomy$fuelType,k)
pcorr[k]=100*sum(FuelEconomy$fuelType==pred)/n
}
pcorr## [1] 83.55474 82.73545 82.41497 82.09707 82.01695 81.85413 81.73783 81.64478
## [9] 81.62669 81.56725library(caret)## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
##
## liftnear5<-data.frame(truetype=FuelEconomy$fuelType[-train],predtype=nearest5)
confusionMatrix(data=nearest5, reference=FuelEconomy$fuelType[-train])## Confusion Matrix and Statistics
##
## Reference
## Prediction CNG Diesel Gasoline or E85
## CNG 0 0 0
## Diesel 0 42 0
## Gasoline or E85 1 0 24
## Gasoline or natural gas 0 0 0
## Gasoline or propane 0 0 0
## Midgrade 0 0 0
## Premium 1 4 7
## Premium and Electricity 0 0 0
## Premium Gas or Electricity 0 0 0
## Premium or E85 0 0 0
## Regular 4 7 48
## Regular Gas and Electricity 0 0 0
## Regular Gas or Electricity 0 0 0
## Reference
## Prediction Gasoline or natural gas Gasoline or propane
## CNG 0 0
## Diesel 0 0
## Gasoline or E85 0 0
## Gasoline or natural gas 0 0
## Gasoline or propane 0 0
## Midgrade 0 0
## Premium 0 1
## Premium and Electricity 0 0
## Premium Gas or Electricity 0 0
## Premium or E85 0 0
## Regular 0 0
## Regular Gas and Electricity 0 0
## Regular Gas or Electricity 0 0
## Reference
## Prediction Midgrade Premium Premium and Electricity
## CNG 0 0 0
## Diesel 0 0 0
## Gasoline or E85 0 7 0
## Gasoline or natural gas 0 1 0
## Gasoline or propane 0 0 0
## Midgrade 5 1 0
## Premium 0 505 2
## Premium and Electricity 0 0 0
## Premium Gas or Electricity 0 0 0
## Premium or E85 0 1 0
## Regular 1 188 3
## Regular Gas and Electricity 0 0 0
## Regular Gas or Electricity 0 0 0
## Reference
## Prediction Premium Gas or Electricity Premium or E85 Regular
## CNG 0 0 0
## Diesel 0 0 5
## Gasoline or E85 0 0 13
## Gasoline or natural gas 0 0 0
## Gasoline or propane 0 0 0
## Midgrade 0 0 1
## Premium 0 4 134
## Premium and Electricity 0 0 0
## Premium Gas or Electricity 0 0 0
## Premium or E85 0 2 0
## Regular 0 2 1485
## Regular Gas and Electricity 0 0 0
## Regular Gas or Electricity 0 0 0
## Reference
## Prediction Regular Gas and Electricity
## CNG 0
## Diesel 0
## Gasoline or E85 0
## Gasoline or natural gas 0
## Gasoline or propane 0
## Midgrade 0
## Premium 1
## Premium and Electricity 0
## Premium Gas or Electricity 0
## Premium or E85 0
## Regular 0
## Regular Gas and Electricity 0
## Regular Gas or Electricity 0
## Reference
## Prediction Regular Gas or Electricity
## CNG 0
## Diesel 0
## Gasoline or E85 0
## Gasoline or natural gas 0
## Gasoline or propane 0
## Midgrade 0
## Premium 0
## Premium and Electricity 0
## Premium Gas or Electricity 0
## Premium or E85 0
## Regular 0
## Regular Gas and Electricity 0
## Regular Gas or Electricity 0
##
## Overall Statistics
##
## Accuracy : 0.8252
## 95% CI : (0.8097, 0.8399)
## No Information Rate : 0.6552
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.6276
##
## Mcnemar's Test P-Value : NA
##
## Statistics by Class:
##
## Class: CNG Class: Diesel Class: Gasoline or E85
## Sensitivity 0.0000 0.7925 0.3038
## Specificity 1.0000 0.9980 0.9913
## Pos Pred Value NaN 0.8936 0.5333
## Neg Pred Value 0.9976 0.9955 0.9776
## Prevalence 0.0024 0.0212 0.0316
## Detection Rate 0.0000 0.0168 0.0096
## Detection Prevalence 0.0000 0.0188 0.0180
## Balanced Accuracy 0.5000 0.8952 0.6476
## Class: Gasoline or natural gas Class: Gasoline or propane
## Sensitivity NA 0.0000
## Specificity 0.9996 1.0000
## Pos Pred Value NA NaN
## Neg Pred Value NA 0.9996
## Prevalence 0.0000 0.0004
## Detection Rate 0.0000 0.0000
## Detection Prevalence 0.0004 0.0000
## Balanced Accuracy NA 0.5000
## Class: Midgrade Class: Premium
## Sensitivity 0.8333 0.7183
## Specificity 0.9992 0.9143
## Pos Pred Value 0.7143 0.7663
## Neg Pred Value 0.9996 0.8924
## Prevalence 0.0024 0.2812
## Detection Rate 0.0020 0.2020
## Detection Prevalence 0.0028 0.2636
## Balanced Accuracy 0.9163 0.8163
## Class: Premium and Electricity
## Sensitivity 0.000
## Specificity 1.000
## Pos Pred Value NaN
## Neg Pred Value 0.998
## Prevalence 0.002
## Detection Rate 0.000
## Detection Prevalence 0.000
## Balanced Accuracy 0.500
## Class: Premium Gas or Electricity Class: Premium or E85
## Sensitivity NA 0.2500
## Specificity 1 0.9996
## Pos Pred Value NA 0.6667
## Neg Pred Value NA 0.9976
## Prevalence 0 0.0032
## Detection Rate 0 0.0008
## Detection Prevalence 0 0.0012
## Balanced Accuracy NA 0.6248
## Class: Regular Class: Regular Gas and Electricity
## Sensitivity 0.9066 0.0000
## Specificity 0.7065 1.0000
## Pos Pred Value 0.8544 NaN
## Neg Pred Value 0.7992 0.9996
## Prevalence 0.6552 0.0004
## Detection Rate 0.5940 0.0000
## Detection Prevalence 0.6952 0.0000
## Balanced Accuracy 0.8065 0.5000
## Class: Regular Gas or Electricity
## Sensitivity NA
## Specificity 1
## Pos Pred Value NA
## Neg Pred Value NA
## Prevalence 0
## Detection Rate 0
## Detection Prevalence 0
## Balanced Accuracy NAConclusion
The k-nearest neighbor method showed that when k=1,the likeliness of correctly classifying the fuel type for a vehicle is 84.4%. It also showed that when k=5,the likeliness of correctly classifying the fuel type for a vehicle is 82.52%. In addition to this, the cross validation showed that the pct for k levels between 1-10 showed that fuel types for vehicles are classified this way 81.62669% to 83.55474% of the time. The kappa value was 0.6276, and fell within a range that was considered substantial. Finally, the accuracy of the confusion matrix was 85.52%, which shows that the prediction of fuel type for a vehicle is accurate 85% of the time.